Q. 38 For each pair of functions f and... [FREE SOLUTION]

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Chapter 4: Q. 38 (page 386)

For each pair of functions f and g and each interval [a, b] in Exercises 38鈥�40, use at least eight rectangles to approximate the area of the region between the graphs of f and g on the interval [a, b]. Your work should include graphs of f and g together with the rectangles that you used.
$f (x) = \sin 鈦� x, g (x) = \cos 鈦� x, [0, 蟺]$

Short Answer

Expert verified

${鈭�}_{0}^{蟺} 鈥� | f (x) 鈭� g (x) | d x = 2.82$

Step by step solution

Step 1. Given information

$f (x) = \sin 鈦� x, g (x) = \cos 鈦� x, [0, 蟺]$

Step 2. Calculating the area

Below is the graph of both functions,

Area between the graphs,

$\begin{aligned} = {鈭�}_{0}^{\frac{蟺}{8}} 鈥� (\cos 鈦� x 鈭� \sin 鈦� x) d x + {鈭�}_{\frac{蟺}{8}}^{\frac{蟺}{4}} 鈥� (\cos 鈦� x 鈭� \sin 鈦� x) d x + {鈭�}_{\frac{蟺}{4}}^{\frac{3 蟺}{8}} 鈥� (\sin 鈦� x 鈭� \cos 鈦� x) d x + {鈭�}_{\frac{3 蟺}{8}}^{\frac{蟺}{2}} 鈥� (\sin 鈦� x 鈭� \cos 鈦� x) d x \\ + {鈭�}_{\frac{蟺}{2}}^{\frac{5 蟺}{8}} 鈥� (\sin 鈦� x 鈭� \cos 鈦� x) d x + {鈭�}_{\frac{蟺}{2}}^{\frac{3 蟺}{4}} 鈥� (\sin 鈦� x 鈭� \cos 鈦� x) d x + {鈭�}_{\frac{3 蟺}{4}}^{\frac{7 蟺}{8}} 鈥� (\sin 鈦� x 鈭� \cos 鈦� x) d x + {鈭�}_{\frac{7 蟺}{8}}^{蟺} 鈥� (\sin 鈦� x 鈭� \cos 鈦� x) d x \\ = 2 (\frac{\sqrt{2}}{2}) + 2 (\frac{\sqrt{2}}{2}) \\ = 2 \sqrt{2} \\ 鈮� 2.828 \end{aligned}$

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Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the area

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